Finite Group Databasebeta

← #27394119

Subgroups — #27394119

Order 13568.

894 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20277201C211yesmaximal, characteristic
2#20275324C211yesmaximal, characteristic, complemented
3#20275323C211yesmaximal, characteristic, complemented
4#20275322C211yesmaximal, characteristic, complemented
5#20275321C211yesmaximal, characteristic, complemented
6#20275320C211yesmaximal, characteristic, complemented
7#20275319C211yesmaximal, characteristic, complemented
8#20275318C211yesmaximal, characteristic, complemented
9#20274698C211yesmaximal, characteristic, complemented
10#20274696C211yesmaximal, characteristic, complemented
11#20274626C211yesmaximal, characteristic
12#20274626C211yesmaximal, characteristic
13C4×#13133129C211yesmaximal, characteristic, complemented
14#20274472C211yesmaximal, characteristic, complemented
15C53×#1923C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C2×#13133174C2211yescharacteristic
18C2×C42×D53C2211yescharacteristic
19C2×C4⋊#88322C2211yescharacteristic
20C2×#13133146C2211yescharacteristic
21C2×#13133146C2211yescharacteristic
22C2×C22⋊#88322C2211yescharacteristic
23C2×C22⋊#88322C2211yescharacteristic
24C2×#13133129C2211yescharacteristic
25C2×#13133129C2211yescharacteristic
26C2×#13133129C2211yescharacteristic
27C2×#13133129C2211yescharacteristic
28C2×#13133129C2211yescharacteristic
29C2×#13133129C2211yescharacteristic
30C2×#13133129C2211yescharacteristic
31C2×#13133129C2211yescharacteristic
32C2×C4×#88322C2211yescharacteristic
33C2×C8×Dic53C2211yescharacteristic
34C2×C8×Dic53C2211yescharacteristic
35#16810527C411yescharacteristic
36#16810527C411yescharacteristic
37#16810523C411yescharacteristic
38#16810523C411yescharacteristic
39#16810501C411yescharacteristic
40#16810501C411yescharacteristic
41#16810499C411yescharacteristic
42#16810499C411yescharacteristic
43C4×#11719921C2211yescharacteristic
44C4×#11719921C2211yescharacteristic
45C4×C22⋊Dic53C2211yescharacteristic
46#16810378C2211yescharacteristic
47#16810378C2211yescharacteristic
48#16810377C2211yescharacteristic
49#16810377C2211yescharacteristic
50#16810377C2211yescharacteristic
51#16810377C2211yescharacteristic
52C2×C4⋊C8×C53C2211yescharacteristic
53C2×C22⋊C8×C53C2211yescharacteristic
54C2×C22⋊C8×C53C2211yescharacteristic
55C2×C4×C8×C53C2211yescharacteristic
56C4×C22⋊C4×C53C2211yescharacteristic
57C53×#336C2211yescharacteristic
58C53×#336C2211yescharacteristic
59C2×#11719945—22no—
60C2×#11719945—22no—
61C2×#11719945—41no—
62C2×#11719945—41no—
63C2×#11719945—41no—
64C2×#11719945—41no—
65C22×Dic106C2×C411yescharacteristic
66C22×D212C2×C411yescharacteristic
67C22×C22⋊D53C2×C411yescharacteristic
68C22×C22⋊D53C2×C411yescharacteristic
69C22×C4×D53C2×C411yescharacteristic
70C22×C4×D53C2×C411yescharacteristic
71C22×C4×D53C2311yescharacteristic
72C22×C4×D53C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77#13133174—41no—
78#13133174—41no—
79C2×#11719919C2×C411yescharacteristic
80C2×#11719919C2×C411yescharacteristic
81C2×C22⋊Dic53C2×C411yescharacteristic
82C2×C22⋊Dic53C2×C411yescharacteristic
83C2×#11719921C2×C411yescharacteristic
84C2×#11719921C2×C411yescharacteristic
85C2×#11719921C2×C411yescharacteristic
86C2×#11719921C2×C411yescharacteristic
87C2×#11719921C2×C411yescharacteristic
88C2×#11719921C2×C411yescharacteristic
89C2×C4×Dic53C2×C411yescharacteristic
90C2×C4×Dic53C2×C411yescharacteristic
91C2×C4×Dic53C2311yescharacteristic
92C2×C4×Dic53C2311yescharacteristic
93C42×D53—41no—
94C42×D53—41no—
95C4⋊#88322—41no—
96#13133146—41no—
97#13133146—41no—
98C22⋊#88322—41no—
99C22⋊#88322—41no—
100#13133129—22no—
101#13133129—22no—
102#13133129—22no—
103#13133129—22no—
104#13133129—41no—
105#13133129—41no—
106#13133129—41no—
107#13133129—41no—
108C4×#88322—41no—
109C8×Dic53—41no—
110C8×Dic53—41no—
111#13133124C2×C411yescharacteristic
112#13133124C2×C411yescharacteristic
113#13133124C2×C411yescharacteristic
114#13133124C2×C411yescharacteristic
115#13133124C2×C411yescharacteristic
116#13133124C2×C411yescharacteristic
117C23×C4×C53C2311yescharacteristic
118C22×C8×C53C2311yescharacteristic
119C22×C8×C53C2311yescharacteristic
120C22×C8×C53C2311yescharacteristic
121C22×C8×C53C2311yescharacteristic
122C2×C22⋊C4×C53C2×C411yescharacteristic
123C2×C22⋊C4×C53C2×C411yescharacteristic
124C2×C42×C53C2311yescharacteristic
125C2×C42×C53C2311yescharacteristic
126C4⋊C8×C53—41no—
127C22⋊C8×C53—41no—
128C22⋊C8×C53—41no—
129C4×C8×C53—41no—
130#95×C53C2×C411yescharacteristic
131#95×C53C2×C411yescharacteristic
132C24×C53C22×C411yescharacteristic
133C23×D53C22×C411yescharacteristic
134C23×D53C22×C411yescharacteristic
135C22×C4×C53—21no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53C22×C411yescharacteristic
142C22×C4×C53C22×C411yescharacteristic
143C22×C4×C53C22×C411yescharacteristic
144C22×C4×C53C22×C411yescharacteristic
145C22×C4×C53C22×C411yescharacteristic
146C22×C4×C53C2411yescharacteristic
147C2×C22⋊D53—22no—
148C2×C22⋊D53—22no—
149C2×C22⋊D53—41no—
150C2×C22⋊D53—41no—
151C2×C22⋊D53—41no—
152C2×C22⋊D53—41no—
153C22×Dic53C22×C411yescharacteristic
154C22×Dic53C22×C411yescharacteristic
155C22×Dic53C22×C411yescharacteristic
156C22×Dic53C22×C411yescharacteristic
157C22×Dic53C22×C411yescharacteristic
158C22×Dic53C22×C411yescharacteristic
159#11719945—44no—
160#11719945—44no—
161#11719945—44no—
162#11719945—44no—
163C2×D212—22no—
164C2×D212—41no—
165C2×D212—41no—
166C2×C4×D53—21no—
167C2×C4×D53—21no—
168C2×C4×D53—21no—
169C2×C4×D53—21no—
170C2×C4×D53—22no—
171C2×C4×D53—22no—
172C2×C4×D53—21no—
173C2×C4×D53—21no—
174C2×C4×D53—21no—
175C2×C4×D53—21no—
176C2×C4×D53—21no—
177C2×C4×D53—21no—
178C2×C4×D53—22no—
179C2×C4×D53—22no—
180C2×C4×D53—41no—
181C2×C4×D53—41no—
182C2×C4×D53#4112yes—
183C2×C4×D53#4112yes—
184C2×Dic106—22no—
185C2×Dic106—41no—
186C2×Dic106—41no—
187C2×C8×C53—21no—
188C2×C8×C53—21no—
189C2×C8×C53—21no—
190C2×C8×C53—21no—
191C2×C8×C53—21no—
192C2×C8×C53—21no—
193C2×C8×C53—21no—
194C2×C8×C53—21no—
195C2×C8×C53—21no—
196C2×C8×C53—21no—
197C2×C8×C53—21no—
198C2×C8×C53—21no—
199C22⋊C4×C53—22no—
200C22⋊C4×C53—22no—
201C42×C53—21no—
202C42×C53—21no—
203C42×C53—21no—
204C42×C53—21no—
205C22⋊Dic53—22no—
206C22⋊Dic53—22no—
207#11719921—22no—
208#11719921—22no—
209#11719921—22no—
210#11719921—22no—
211#11719921—41no—
212#11719921—41no—
213#11719919—41no—
214#11719919—41no—
215C4×Dic53—21no—
216C4×Dic53—21no—
217C4×Dic53—21no—
218C4×Dic53—21no—
219C4×Dic53—41no—
220C4×Dic53—41no—
221C2×#88322—21no—
222C2×#88322—21no—
223C2×#88322—21no—
224C2×#88322—21no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C23×C53—21no—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53C23×C411yescharacteristic
241C22×D53—21no—
242C22×D53—21no—
243C22×D53—21no—
244C22×D53—21no—
245C22×D53—21no—
246C22×D53—21no—
247C22×D53—21no—
248C22×D53—21no—
249C22×D53—21no—
250C22×D53—21no—
251C22×D53—21no—
252C22×D53—21no—
253C22×D53—21no—
254C22×D53#11712yes—
255C2×C4×C53—21no—
256C2×C4×C53—21no—
257C2×C4×C53—21no—
258C2×C4×C53—21no—
259C2×C4×C53—21no—
260C2×C4×C53—21no—
261C2×C4×C53—21no—
262C2×C4×C53—21no—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—41no—
271C2×C4×C53—41no—
272C2×C4×C53#13112yes—
273C2×C4×C53#13112yes—
274C2×C4×C53C2×#4111yescharacteristic
275C2×C4×C53C2×#4111yescharacteristic
276C2×C4×C53H(5,𝔽2)11yescharacteristic
277C2×C4×C53H(5,𝔽2)11yescharacteristic
278C2×C4×C53H(5,𝔽2)11yescharacteristic
279C2×C4×C53H(5,𝔽2)11yescharacteristic
280C22⋊D53—44no—
281C22⋊D53—44no—
282C2×Dic53—21no—
283C2×Dic53—21no—
284C2×Dic53—21no—
285C2×Dic53—21no—
286C2×Dic53—21no—
287C2×Dic53—21no—
288C2×Dic53—21no—
289C2×Dic53—21no—
290C2×Dic53—21no—
291C2×Dic53—21no—
292C2×Dic53—21no—
293C2×Dic53—21no—
294C2×Dic53—21no—
295C2×Dic53—21no—
296C2×Dic53—21no—
297C2×Dic53#11712yes—
298C2×Dic53#13112yes—
299C2×Dic53#13112yes—
300D212—44no—
301C4×D53—22no—
302C4×D53—22no—
303C4×D53—22no—
304C4×D53—22no—
305C4×D53—44no—
306C4×D53—44no—
307C4×D53—41no—
308C4×D53—41no—
309C4×D53—41no—
310C4×D53—41no—
311Dic106—44no—
312C8×C53—41no—
313C8×C53—41no—
314C8×C53—41no—
315C8×C53—41no—
316#88322—41no—
317#88322—41no—
318#88322—41no—
319#88322—41no—
320#21903—531nomaximal, Sylow
321C22×C53—41no—
322C22×C53—41no—
323C22×C53—41no—
324C22×C53—41no—
325C22×C53—41no—
326C22×C53—41no—
327C22×C53—41no—
328C22×C53C2×#11711yescharacteristic
329C22×C53#51811yescharacteristic
330C22×C53#51811yescharacteristic
331C22×C53C2×#13111yescharacteristic
332C22×C53C2×#13111yescharacteristic
333C22×C53C2×#13111yescharacteristic
334C22×C53C2×#13111yescharacteristic
335C2×D53—22no—
336C2×D53—22no—
337C2×D53—22no—
338C2×D53—41no—
339C2×D53—41no—
340C2×D53—41no—
341C2×D53—41no—
342C2×D53—41no—
343C2×D53—41no—
344C2×D53—41no—
345C2×D53—41no—
346C2×D53—41no—
347C2×D53—41no—
348C2×D53—41no—
349C4×C53—22no—
350C4×C53—22no—
351C4×C53—41no—
352C4×C53—41no—
353C4×C53—41no—
354C4×C53#53811yescharacteristic
355C4×C53#53811yescharacteristic
356C4×C53#53811yescharacteristic
357C4×C53#53811yescharacteristic
358Dic53—22no—
359Dic53—22no—
360Dic53—22no—
361Dic53—41no—
362Dic53—41no—
363Dic53—41no—
364#2297—531no—
365#1923—531no—
366#1923—531no—
367#1923—531no—
368#1923—531no—
369#1923—531no—
370#1923—531no—
371#1923—531no—
372#1923D5311yescharacteristic, complemented
373#1798—531no—
374#1798—531no—
375#1780—531no—
376#1780—531no—
377C4×C22⋊C8—531no—
378C4×C22⋊C8—531no—
379C2×C53—81no—
380C2×C53#231211yescharacteristic
381C2×C53#292211yescharacteristic
382C2×C53#292211yescharacteristic
383C2×C53#297711yescharacteristic
384C2×C53#297711yescharacteristic
385C2×C53#297911yescharacteristic
386C2×C53#297911yescharacteristic
387D53—42no—
388D53—81no—
389C22×#41—531no—
390C2×#117—531no—
391C22×C42—531no—
392C2×C4⋊C8—531no—
393C2×C4⋊C8—531no—
394C2×C4⋊C8—531no—
395C2×C4⋊C8C2×D5311yescharacteristic
396C2×C22⋊C8—531no—
397C2×C22⋊C8—531no—
398C2×C22⋊C8—531no—
399C2×C22⋊C8—531no—
400C2×C22⋊C8—531no—
401C2×C22⋊C8—531no—
402C2×C22⋊C8—531no—
403C2×C22⋊C8—531no—
404C2×C22⋊C8—531no—
405C2×C22⋊C8—531no—
406C2×C22⋊C8C2×D5311yescharacteristic
407C2×C22⋊C8C2×D5311yescharacteristic
408C2×C4×C8—531no—
409C2×C4×C8—531no—
410C2×C4×C8—531no—
411C2×C4×C8C2×D5311yescharacteristic
412#391—531no—
413#391—531no—
414#390—531no—
415#390—531no—
416#386—531no—
417#386—531no—
418#386—531no—
419#386—531no—
420C4×C22⋊C4—531no—
421C4×C22⋊C4—531no—
422C4×C22⋊C4—531no—
423C4×C22⋊C4C2×D5311yescharacteristic
424#336—531no—
425#336—531no—
426#336—531no—
427#336—531no—
428#336—531no—
429#336—531no—
430#336C2×D5311yescharacteristic
431#336C2×D5311yescharacteristic
432C53#2190311yescharacteristic, complemented, Sylow
433C2×#41—1062no—
434C2×#41—1062no—
435C2×#41—2121no—
436C2×#41—2121no—
437C2×#41—2121no—
438C2×#41—2121no—
439C22×Q8—531no—
440C22×D4—531no—
441C22×D4—531no—
442C22×D4—531no—
443C23×C4—531no—
444C23×C4—531no—
445C23×C4—531no—
446C23×C4—531no—
447C23×C4C22×D5311yescharacteristic
448C22×C8—531no—
449C22×C8—531no—
450C22×C8—531no—
451C22×C8—531no—
452C22×C8C22×D5311yescharacteristic
453C22×C8C22×D5311yescharacteristic
454C22×C8C22×D5311yescharacteristic
455C22×C8C22×D5311yescharacteristic
456#117—2121no—
457#117—2121no—
458C2×C4⋊C4—531no—
459C2×C4⋊C4—531no—
460C2×C22⋊C4—531no—
461C2×C22⋊C4—531no—
462C2×C22⋊C4—531no—
463C2×C22⋊C4—531no—
464C2×C22⋊C4—531no—
465C2×C22⋊C4—531no—
466C2×C22⋊C4—531no—
467C2×C22⋊C4—531no—
468C2×C22⋊C4C4×D5311yescharacteristic
469C2×C22⋊C4C4×D5311yescharacteristic
470C2×C42—531no—
471C2×C42—531no—
472C2×C42—531no—
473C2×C42—531no—
474C2×C42—2121no—
475C2×C42—2121no—
476C2×C42C22×D5311yescharacteristic
477C2×C42C22×D5311yescharacteristic
478C4⋊C8—41no—
479C4⋊C8—2121no—
480C4⋊C8—2121no—
481C4⋊C8—2121no—
482C22⋊C8—41no—
483C22⋊C8—41no—
484C22⋊C8—1062no—
485C22⋊C8—1062no—
486C22⋊C8—1062no—
487C22⋊C8—1062no—
488C22⋊C8—2121no—
489C22⋊C8—2121no—
490C22⋊C8—2121no—
491C22⋊C8—2121no—
492C22⋊C8—2121no—
493C22⋊C8—2121no—
494C4×C8—41no—
495C4×C8—2121no—
496C4×C8—2121no—
497C4×C8—2121no—
498#95—531no—
499#95—531no—
500#95—531no—
501#95—531no—
502#95—531no—
503#95—531no—
504#95C4×D5311yescharacteristic
505#95C4×D5311yescharacteristic
506C24—531no—
507C24—531no—
508C24C2×C4×D5311yescharacteristic
509#41—2124no—
510#41—2124no—
511#41—2124no—
512#41—2124no—
513C2×Q8—1062no—
514C2×Q8—2121no—
515C2×Q8—2121no—
516C2×D4—1062no—
517C2×D4—1062no—
518C2×D4—1062no—
519C2×D4—2121no—
520C2×D4—2121no—
521C2×D4—2121no—
522C2×D4—2121no—
523C2×D4—2121no—
524C2×D4—2121no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—531no—
532C22×C4—531no—
533C22×C4—531no—
534C22×C4—532no—
535C22×C4—532no—
536C22×C4—531no—
537C22×C4—531no—
538C22×C4—531no—
539C22×C4—1062no—
540C22×C4—1062no—
541C22×C4—1061no—
542C22×C4—1061no—
543C22×C4—1061no—
544C22×C4—1061no—
545C22×C4—1062no—
546C22×C4—1062no—
547C22×C4—1061no—
548C22×C4—1061no—
549C22×C4—1061no—
550C22×C4—1061no—
551C22×C4—1061no—
552C22×C4—1061no—
553C22×C4—2121no—
554C22×C4—2121no—
555C22×C4C2×C4×D5311yescharacteristic
556C22×C4C2×C4×D5311yescharacteristic
557C22×C4C2×C4×D5311yescharacteristic
558C22×C4C2×C4×D5311yescharacteristic
559C22×C4C2×C4×D5311yescharacteristic
560C22×C4C23×D5311yescharacteristic
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—1061no—
574C2×C8—1061no—
575C2×C8—1061no—
576C2×C8—1061no—
577C2×C8—1061no—
578C2×C8—1061no—
579C2×C8—1061no—
580C2×C8—1061no—
581C2×C8—1061no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C4⋊C4—2121no—
586C4⋊C4—2121no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—1062no—
590C22⋊C4—1062no—
591C22⋊C4—1062no—
592C22⋊C4—1062no—
593C22⋊C4—1062no—
594C22⋊C4—1062no—
595C22⋊C4—2121no—
596C22⋊C4—2121no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—1061no—
602C42—1061no—
603C42—1061no—
604C42—1061no—
605C42—2121no—
606C42—2121no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—532no—
615C23—1061no—
616C23—1061no—
617C23—1061no—
618C23—1061no—
619C23—1061no—
620C23—1061no—
621C23—1061no—
622C23—1061no—
623C23—1061no—
624C23—1061no—
625C23—1061no—
626C23—1061no—
627C23—1061no—
628C23C22×C4×D5311yescharacteristic
629Q8—2124no—
630D4—2124no—
631D4—2124no—
632D4—2124no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—532no—
651C2×C4—532no—
652C2×C4—532no—
653C2×C4—1061no—
654C2×C4—1061no—
655C2×C4—1061no—
656C2×C4—1061no—
657C2×C4—1061no—
658C2×C4—1061no—
659C2×C4—1062no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1061no—
664C2×C4—1061no—
665C2×C4—1061no—
666C2×C4—1061no—
667C2×C4—1061no—
668C2×C4—1061no—
669C2×C4—1061no—
670C2×C4—1061no—
671C2×C4—1061no—
672C2×C4—2124no—
673C2×C4—2124no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4#1313322312yes—
679C2×C4#1313322512yes—
680C2×C4#41×D5311yescharacteristic
681C2×C4#41×D5311yescharacteristic
682C2×C4#1313326211yescharacteristic
683C2×C4#1313326211yescharacteristic
684C2×C4#1313326311yescharacteristic
685C2×C4#1313326311yescharacteristic
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—2121no—
691C8—2121no—
692C8—2121no—
693C8—2121no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—1062no—
702C22—1062no—
703C22—1062no—
704C22—2121no—
705C22—2121no—
706C22—2121no—
707C22—2121no—
708C22—2121no—
709C22—2121no—
710C22—2121no—
711C22—2121no—
712C22—2121no—
713C22—2121no—
714C22—2121no—
715C22#117×D5311yescharacteristic
716C22#1681109511yescharacteristic
717C22#1681109511yescharacteristic
718C22#131×D5311yescharacteristic
719C22#131×D5311yescharacteristic
720C22C2×#1313322311yescharacteristic
721C22C2×#1313322511yescharacteristic
722C4—22no—
723C4—22no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—1062no—
728C4—1062no—
729C4—1062no—
730C4—2121no—
731C4—2121no—
732C4—2121no—
733C4#1681120511yescharacteristic
734C4#1681120711yescharacteristic
735C4#1681120911yescharacteristic
736C4#1681121211yescharacteristic
737C2—81no—
738C2—4241no—
739C2—2122no—
740C2#2027730911yescharacteristic
741C2#2028335411yescharacteristic
742C2#2028335611yescharacteristic
743C2#2028376611yescharacteristic
744C2#2028376811yescharacteristic
745C2#2028377811yescharacteristic
746C2#2028378011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1923C2
prime radicalC22×#11719945C22
cosocleC22×C4×C53C24
hypercenter#1923D53
hypocenterC53#21903
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1923

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20275324C2semidirect
3. #20275323C2semidirect
4. #20275322C2semidirect
5. #20275321C2semidirect
6. #20275320C2semidirect
7. #20275319C2semidirect
8. #20275318C2semidirect
9. #20274698C2semidirect
10. #20274696C2semidirect
13. C4×#13133129C2semidirect
14. #20274472C2semidirect
15. C53×#1923C2semidirect
372. #1923D53semidirect
432. C53#21903semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202772012
#202753242
#202753232
#202753222
#202753212
#202753202
#202753192
#202753182
#202746982
#202746962
#202746262
C4×#131331292
#202744722
C53×#19232
#2190353